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Differential uniformity and the associated codes of cryptographic functions
A network reliability approach to the analysis of combinatorial repairable threshold schemes
David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada |
A repairable threshold scheme (which we abbreviate to RTS) is a $ (\tau,n) $-threshold scheme in which a subset of players can "repair" another player's share in the event that their share has been lost or corrupted. This will take place without the participation of the dealer who set up the scheme. The repairing protocol should not compromise the (unconditional) security of the threshold scheme. Combinatorial repairable threshold schemes (or combinatorial RTS) were recently introduced by Stinson and Wei [
References:
[1] |
J. Benaloh and J. Leichter, Generalized secret sharing and monotone functions, Lecture Notes in Computer Science, 403 (1990), 27-35 (CRYPTO '88 Proceedings).
doi: 10.1007/0-387-34799-2_3. |
[2] |
C. J. Colbourn, The Combinatorics of Network Reliability, Oxford University Press, 1987.
![]() |
[3] |
C. J. Colbourn and J. H. Dinitz, Handbook of Combinatorial Designs, Second Edition, Chapman & Hall/CRC, Boca Raton, FL, 2007. |
[4] |
B. Kacsmar, Designing Efficient Algorithms for Combinatorial Repairable Threshold Schemes, Masters Thesis, University of Waterloo, 2018. Google Scholar |
[5] |
T. M. Laing and D. R. Stinson,
A survey and refinement of repairable threshold schemes, Journal of Mathematical Cryptology, 12 (2018), 57-81.
doi: 10.1515/jmc-2017-0058. |
[6] |
A. Shamir,
How to share a secret, Communications of the ACM, 22 (1979), 612-613.
doi: 10.1145/359168.359176. |
[7] |
D. R. Stinson and M. B. Paterson, Cryptography. Theory and Practice, Chapman & Hall/CRC, Boca Raton, 2019. Google Scholar |
[8] |
D. R. Stinson and R. Wei,
Combinatorial repairability for threshold schemes, Designs, Codes and Cryptography, 86 (2018), 195-210.
doi: 10.1007/s10623-017-0336-6. |
show all references
References:
[1] |
J. Benaloh and J. Leichter, Generalized secret sharing and monotone functions, Lecture Notes in Computer Science, 403 (1990), 27-35 (CRYPTO '88 Proceedings).
doi: 10.1007/0-387-34799-2_3. |
[2] |
C. J. Colbourn, The Combinatorics of Network Reliability, Oxford University Press, 1987.
![]() |
[3] |
C. J. Colbourn and J. H. Dinitz, Handbook of Combinatorial Designs, Second Edition, Chapman & Hall/CRC, Boca Raton, FL, 2007. |
[4] |
B. Kacsmar, Designing Efficient Algorithms for Combinatorial Repairable Threshold Schemes, Masters Thesis, University of Waterloo, 2018. Google Scholar |
[5] |
T. M. Laing and D. R. Stinson,
A survey and refinement of repairable threshold schemes, Journal of Mathematical Cryptology, 12 (2018), 57-81.
doi: 10.1515/jmc-2017-0058. |
[6] |
A. Shamir,
How to share a secret, Communications of the ACM, 22 (1979), 612-613.
doi: 10.1145/359168.359176. |
[7] |
D. R. Stinson and M. B. Paterson, Cryptography. Theory and Practice, Chapman & Hall/CRC, Boca Raton, 2019. Google Scholar |
[8] |
D. R. Stinson and R. Wei,
Combinatorial repairability for threshold schemes, Designs, Codes and Cryptography, 86 (2018), 195-210.
doi: 10.1007/s10623-017-0336-6. |
size | type | expected number |
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3 | pair-point-point | |
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size | type | expected number |
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3 | pair-pair-pair | |
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